Question

sec alpha = 5/4, find value of tan alpha/1 + tan square alpha

Answer 1

Answer on Question #68512 Math / Trigonometry

sec alpha = 5/4, find value of tan alpha/1 + tan square alpha

Solution:

$$\sec \alpha = \frac {5}{4}$$ $$\cos \alpha = \frac {1}{\sec \alpha} = \frac {4}{5}, \sin \alpha = \sqrt {1 - \cos^ {2} \alpha} = \sqrt {1 - \left(\frac {4}{5}\right) ^ {2}} = \frac {3}{5}.$$ $$\tan \alpha = \frac {\sin \alpha}{\cos \alpha} = \frac {3}{4}$$

So

$$\frac {\tan \alpha}{1 + \tan^ {2} \alpha} = \frac {\frac {3}{4}}{1 + \left(\frac {3}{4}\right) ^ {2}} = \frac {12}{25} = 0.48$$

Answer: $\frac{12}{25} = 0.48$

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